Difficulties: This
text is a translation of an appropriate text (written in June 1996) which is
partial. I am writing a more general text.I give the same
meaning to two couple of notions: a) “matématiques modernes” and “Whole Math”
and b) the avatars of present (from 1980) French reform and the New New Math in
the USA: I’ll hope there will be no misunderstandings.

According to the
accounts from French teachers who taught in the US in the mid 80’s, the
American average mathematics standard was lower than the French one, but it’s
difficult to use the term “average” for the USA as standards and curriculums
are not centralized state’s obligations as in France.

About the problem of
New Math, I only know one text in English by Rene THOM: “Modern mathematics: an
educational and philosophical error?” American Scientist, 59,6 p 695. But there
are other excellent texts from the 70’s on the subject by the same in French:
I‘ll try to translate, or, better, I’ll scan them if you find a translator in
the USA.

The pupils’ math
standards, which formed the Certificate of Primary School, are going down.
Regarding the field into which we could interfere and which does not certainly
depend on families which are not to blame - those teachers’ arguments against
family’s responsibility and against the previous grade teachers’ skills are
used to justify the servile attitude of the teaching staff in relation to its authority-
this fall is essentially due to several factors:

First, the constant
change of the curriculum which, for instance, forbids generations to help each
other (but increases the market for new books in schools, for home education
products and remedial courses). Is a straight line the shortest distance
between two points or “the set of the affine bijections from R to R”? For your
information, in the 70’s, the “set theory” and the bijection were necessary to
“develop the mind” of the sixth grade pupils (and even pupils of the primary
school) but nowadays they are only partly studied in the scientific 11th and
12th grades.

This only fact shows
the inextricable situation of the French Education State Department: they
simultaneously want to suppress important parts of the curriculum and show a
rising of standard of education. In the same way, why is the rule of three
forbidden in the 70’s and why are the proportional tables imposed to deal with
the same problems? Here I stop giving examples because I am not attending a
thesis. I do not neglect the contribution of modern mathematics but, according
to me, they seem to allow solving problem, which are to be found neither in
primary school nor in junior high school. In one sense, acting with a good
intention against the previous formalism, the central aim of modern mathematics
introduction in school was hyper-rationalist philosophy: nobody can learn 2+2=4
without understanding group theory and calculus in all bases; but “ratio” is
against the instinct which is the basis of pedagogic intervention. We can find
the same rationalistic approach in the New New Math where a pupil, in one
sense, must find again by himself all the knowledge of the past.

Secondly, one of the
main factors is the very content of those curriculums. We have gone from the
period of “Whole Math” to the one of the 80’s reform.

Whole Math (70’s)

Roughly speaking, the
contents of the “mathématiques modernes” period (1970 -80), with the formal and
the structure put forward, was:

- in arithmetic, the non-necessity
to learn to calculate ( it was before the pocket calculators). It was the basis
era when we learnt that 3+2 could be 10 or 11 before knowing how to give change
and without knowing the tables of operations by heart. From which mockery about
arithmetic old fashion problems began: those problems have derisively been
called “leaking tap problems” whereas they are essential because they allow
learning the complexity of the basic mathematics tools in a simplified
situation. . The latter is introduced as artificial ( and not concrete) without
noticing that the real situation presents “physics’ rubbings” which are not
controllable in a training situation ( try to calculate the volume of my
“concrete” shoe!!). This non-necessity quickly transformed itself in a fall of
calculus skills....

- in geometry : under
the pretext that a straight line could not be straight ( also true for other
basic figures), the primary school has a bad knowledge of basic figures.. Also
under the pretext of the discovery of the invariant elements in the geometric
group theory, the teaching of what was a basis of learning of proof is
eliminated and forbidden : I mean the “ 3 cas d’égalités des triangles” - in
English, I think, SSS, SAS and ASA congruence postulates - which indeed is
unperfected in the absolute but largely adequate and very efficient for a
junior high School pupil. So this teaching is eliminated to be replaced by the
use of transformations (symmetry, rotation) which is per se more difficult to
use in many situations and that an 8th grade pupil is not able to control. They
had better made friezes that teach as much for the invariant elements..

The reform of the
reform ( 1980 up to ?)

Instead of adjusting
one’s sights by explaining the errors that had been made - unthinkable- , the
education authority which wrote the previous curriculum, takes half-measures in
order to be adequate to the new low skill and so they reinforce a new fall in
skills. In arithmetic, the possibility to use the pocket calculator helps to justify
the drop in math standards. and last year, during an educational conference, an
expert in education explained that asking a 6th grade pupil to divide 4374 by
532 or 2.37 by 0.564 , was a “virtuous exercise” which besides was forbidden.
The present 6th grade curriculum requires the maximum skills to “ calculate the
quotient and the remainder of a whole number by a two digits’ whole
number...... In simple cases -???- , divide a decimal number by a whole
number.... ” . That’s all : without any protest from any teachers unions,
parents association or press article : in this case, silence is as demagogic as
criminal. We could expect that the new 7th grade curriculum enable the pupils
to divide 5.3 by 4.12: not at all and silence on this subject. The required standard
is going down but Baudelot (a publicist) and the national department of
statistics for education ( DEP : “Direction de l’Evaluation et de la
Perspective”) will show , in spite of all, that the standard is going up and
those who deny it are chilly and inflexible reactionaries who are afraid of
change. The fall in math standards would no more allow to teach arithmetic (
prime numbers) in the 7th grade ( it was a part of curriculum for over a
century). The educrat’s solution was simple : they suppressed it in the whole
secondary school. In geometry, I will not come back to triangles congruence
postulates but for instance, calculating the area of a circle is now part of
the 7th grade curriculum when it was previously in the 5th grade . I think that
, removing any reference to this item in comparison with older statistics
series, the DEP will, one more time, show that the standard is going up. Who
will stop the crazy machine? Generally speaking, the new reform, which is more
demagogic, does not forbid expressly anymore the rule of three nor the
triangles congruent postulates just because a great deal of the new teachers
have not been taught and trained during their own Junior School cursus ( only
the teachers who are 35/40 and more know them and, after 25 years of various
reforms, it is not possible to decide individually to teach them ) but the ban
remains on division because precisely all the teachers still know how to do a
division.

An anecdote for the
end

Yesterday, December
3rd 1997, I took part in a pedagogic conference and, hiding the cover of a
booklet, I read the following text : “ I consider that making mathematics is
not to show calculations skills (algebraic or arithmetic), even if, up to the
last days, those know how were indispensable for mathematics arguments. As
calculus tools were not existing, we must use mental and hand calculus ( with
lost time, origins of errors, forgetting of the aim of the problem) .....During
20 seculars, it’s that manner which had prevailed (it is normal that it left
indelible aftermath)..... I have no doubts about the fact that “mechanization”
of calculus will become an habit”. And I asked : “Who wrote that?”. The answer
of the person in charge of the meeting was interesting . He knew that I tried
to trap him and said : “I know that you try to trap us but, perhaps an
Education Secretary ...” . The essential is that a pedagogic manager is not
spontaneously able to distinguish a pedagogic text and an advertisement for the
Casio pocket calculators. It’s funnier in France than in the USA : teachers -
and in particular this manager - are politically left and their credo is to
protect the state school - “L’Ecole Laïque”- against capitalism, market and
economic liberalism. This shows the standard level of the pedagogic speech
after 25 years of Whole and New New math.

1997/12/04

Michel Delord

Note on TIMMS :

Mr. Roger Fauroux,
chairman of Saint Gobain, says in the October 1997 issue of “Capital”: “
Recently a mathematics test had shown that France was 13th, behind Singapore
and the South Korea. The Senior Civil Servants of the DEP are not speaking
about this result: in 1994, after they had accepted to take part in an OCDE
international test, they silently left after having seen the first results”.
And if you look at the TIMMS results , you can see that there is no French
results for the 4th grade test. Mr. Fauroux in the “ Rapport Fauroux ” proposed
last year a reform which put forward the basic skills : for many reasons,
saying that it is insufficient - the school needs first “democracy” or
“culture”.... - all the French educrats and experts in pedagogy avoid the
subject : it’s important to notice that in France all those experts are paid
and employed by French Department of Education and that Mr. Fauroux in his
report asks for an independent and international control of the pupils skills.